This invention relates generally to plasma sources. More particularly, it relates to linear geometry Hall plasma sources.
Hall discharge plasma accelerators have been considered for use in satellite propulsion since the early 1960""s (see C. O. Brown and E. A. Pinsley, AIAA J. 3, 853, 1965, and G. S. Janes and R. S. Lowder, Phys. Fluids 9, 1115, 19966). In a Hall plasma source, a low-pressure discharge is sustained within a bounded dielectric channel in crossed electric and magnetic fields. Electrons emitted from a cathode external to the channel, or created by the ionization processes, drift along the channel towards the anode located at the channel base. The anode also serves as the source of neutral propellant particles (typically xenon atoms). A radial component to the magnetic field is designed to be a maximum near the channel exit, and in this region the electrons become highly magnetized, as the classical electron Hall parameter is much greater than unity.
FIG. 1A is a cross-sectional schematic representation of a conventional Hall discharge plasma source 10, having a coaxial geometry rotationally symmetric about an axis 104. FIG. 1B is an axial view of conventional Hall discharge plasma source 10 taken along axis 104 of FIG. 1A. Coaxial Hall discharge plasma source 10 has an annular channel 102, within which surrounding solenoids 106, 108 generate a radial magnetic field B. An electric field E is generated in an axial direction 122 within annular channel 102 between an anode 110 at the base 114 of annular channel 102 and a cathode 112 external to annular channel 102. In this coaxial configuration, electrons are constrained to move in the azimuthal direction (indicated by arrows 152) of a closed Exc3x97B drift, with cross-field drift providing the necessary electron current to sustain the discharge. As the electron Hall parameter (the product of the electron cyclotron frequency, xcfx89ce=eB/me, and the mean time between electron collisions xcfx84, where e is the electron charge, me is the electron mass, and B is the radial magnetic field), is much greater than unity, the Hall current density (the product of the electron charge e, the local number of electrons per unit volume ne, and the electron Hall drift velocity Ved=E/B, where E is the axial electric field) can be many orders of magnitude greater than the axial current density (the Hall current density divided by the Hall parameter). According to classical electron transport theory, electrons can circle annular channel 102 in the Hall (azimuthal) direction 152 many times before being captured at anode 110. Anode 110 also serves as the source of neutral propellant particles 111 (typically xenon atoms). A coaxial geometry allows for a xe2x80x9cclosedxe2x80x9d electron drift in the Hall direction, and uninterrupted Hall current. The region of electrons thus trapped acts as a volumetric zone of ionization 113 that in some devices may occupy only a small fraction of the overall channel depth D. Ions 120 are generated in the volumetric zone of ionization 113 by collisions of neutral propellant particles 111 with the trapped electrons. Ions 120, substantially unaffected by magnetic field B because of their large inertia, are accelerated by electric field E resulting from the impeded electron flow (the resistance to the flow of electrons as a result of the applied magnetic field), producing thrust. Accelerated ions 120 recombine with available electrons in the region external to channel 102 to provide a source of high thrust neutral particles 121. Very high ionization fractions and ion velocities can be generated with these discharges. Accordingly, due to their high efficiencies and high specific impulse (the resulting ion velocity divided by the gravity constant 9.8 m/s2), coaxial Hall discharge plasma sources 10 in the 1-5 kW power range are being evaluated as plasma thrusters for use on commercial, military, and research spacecraft (see F. S. Gulczinski and R. A. Spores, xe2x80x9cAnalysis of Hall-Effect Thrusters and Ion Engines for Orbit Transfer Missions,xe2x80x9d AIAA-96-2973, 32nd Joint Propulsion Conference, Jul. 1-3, 1996, Lake Buena Vista, Fla.).
A precise theory is lacking for the mechanism of cross-field electron transport in Hall plasma thrusters. Early experiments on Hall plasma sources indicated that classical electron transport theory could not account for the measured xe2x80x9canomalousxe2x80x9d axial (cross-field) electron current densities. Janes and Lowder (cited above) drew attention to the presence of density and electric field fluctuations within the channel of a Hall discharge, and first suggested that these plasma disturbances enhance the axial electron current. Indirect measurements of the xe2x80x9ceffectivexe2x80x9d Hall parameter as a result of these fluctuations were in agreement with the anomalous transport coefficient first identified by Bohm et al. (see D. Bohm, in The Characteristics of Electrical Discharges in Macnetic Fields, A. Guthrie and R. K. Wakerling, Eds., McGraw Hill, N.Y., 1949) which characterizes the process now widely recognized as xe2x80x9canomalousxe2x80x9d Bohm diffusion (see F. F. Chen, Plasma Physics and Controlled Fusion, 2nd Edition, Plenum Press, NY, p. 193, 1985). The Bohm mechanism predicts an electron mobility that scales inversely with the magnetic field strength (as opposed to the classical Bxe2x88x922 scaling), and an effective electron Hall parameter of about 16. At conditions typical of coaxial Hall plasma thrusters near the region where the magnetic field is strongest, the classical Hall parameter is about 500-1000. A value of 16 represents a significant enhancement in the cross-field drift, and indicates that the ratio of Hall current density to axial current density may be much less than that suggested by classical transport theory.
Whereas an enhanced electron current due to fluctuations is one possible mechanism for enhanced electron transport, the operation of modern Hall plasma thrusters seems to depend significantly on the properties of dielectric channel walls 116 (see Raitses et al., cited above). Previous researchers have proposed the possibility of an enhanced xe2x80x9cnear-wall conductivityxe2x80x9d due to the xe2x80x9cwall scatteringxe2x80x9d of electrons. Whereas it seems that precise knowledge of which mechanism is responsible for transport is necessary to properly scale a Hall discharge is lacking, it is shown below that either of these mechanisms exhibits the necessary dependency on discharge parameters to achieve a desired scaling in discharge size or power.
Modern coaxial Hall plasma thrusters 10 that operate in the 1-5 kW power range have been shown to operate with very high thrust efficiencies in the range of approximately 50%. These thrusters have annular acceleration channel diameters 2R ranging from 50 to 280 mm. One feature common to these thrusters is that channel width W is approximately 15% of channel diameter 2R, which itself is about twice the acceleration channel depth D. In scaling these discharges to operate at various power ranges, it is often desirable to preserve a geometrical relationship between channel width W, diameter 2R, and depth D, although the physical basis for the commonly used geometrical relationships is not well understood.
In a coaxial Hall thruster 10, the magnetic field B near a channel exit face 118 is sufficient to trap the electrons in an orbital cyclotron motion 130, in a plane orthogonal to magnetic field B. The electron orbit radius re (xe2x80x9cLarmor radiusxe2x80x9d) is generally smaller than the electron mean free path xcex and the acceleration channel width W. In this way, the electrons are confined to the magnetized portion of the plasma discharge. The Larmor radius, being dependent on particle mass, is much larger for ions, which are substantially unaffected by the magnetic field. The electron Larmor radius, re, scales as:                               r          e                ∼                                            T              e                              1                /                2                                      B                    .                                    (        1        )            
Here B is the magnetic field strength and Te is the electron temperature. In the design of a low power (and hence presumably smaller) discharge, a decrease in W requires a corresponding decrease in re. The magnetic field strength can be tailored for proper scaling; however, the electron temperature is not easily adjusted, as it is a consequence of a more complex relationship between geometry and operating conditions. The electron temperature is established through a balance between ohmic dissipation, electron-particle collisions (including ionization), and electron-wall collisions. Another approach is to scale the magnetic field strength as necessary and apply reasonable scaling arguments to preserve the mean electron energy from one design to another. It is seen from Eqn. (1) that, if the electron temperature is to be preserved in scaling to lower powers, reducing the characteristic size of the thruster requires a concomitant increase in the operating magnetic field strength.
In a Hall discharge""s use as a propulsion device, it is desirable to efficiently utilize the propellant, by achieving as high an ionization fraction possible. In scaling a higher-power Hall discharge to lower powers, it is therefore desirable to preserve the ratio of the characteristic time to ionize the propellant to the residence time of the propellant in the discharge channel. The ionization time can be found from the inverse of the volumetric rate of ionization Ri, which scales linearly as the electron and neutral densities (ne and na):
Ri=nenaxcex1i(Te).xe2x80x83xe2x80x83(2)
Here, (xcex1i(Te) is the temperature-dependent electron impact ionization rate coefficient. The characteristic time for ionization is xcfx84i=ne/Ri:
xcfx84i=1/naxcex1i.xe2x80x83xe2x80x83(3)
The residence time for a neutral atom can be found by dividing the acceleration channel depth D by the velocity of the neutrals, so it is expected to scale as:
xcfx84Rxcx9cD/Ta1/2.xe2x80x83xe2x80x83(4)
Here, Ta is the neutral xenon temperature, which is typically assumed to be relatively uniform, and which largely controls the gasdynamic behavior of the neutral particles within the channel. The ratio of these two parameters, the ionization time over the residence time, scales as:                                                         τ              R                                      τ              i                                ∼                      Dn            a                          ,                            (        5        )            
wherein it is assumed that the neutral xenon temperature (along with the electron temperature) is invariant to scale. This assumption regarding the invariance in Ta may be tenuous, since the xenon temperature depends on the anode and channel wall temperatures, both of which are likely to be considerably higher for a low power device, because of the geometric scaling conclusions described below. A consequence of Eqn. (5) is that a geometric reduction in the channel depth requires a corresponding increase in the neutral particle density to preserve the ratio of time scales. As described below, this density increase is achieved by properly scaling the mass flow rate and the channel area.
The axial variation in the magnetic field also produces a significant impact on discharge performance. In a modern coaxial Hall thruster, the radial magnetic field is sharply peaked near the exit of the acceleration channel, with a distribution width that is much less then the channel depth. A high magnetic field near the anode can lead to a large anode fall loss as electrons experience resistance to current flow.
Since magnetic fields are difficult to shape, especially for coaxial designs, the depth of the channel is often dictated more by the magnetic field distribution than geometric scaling of the channel length.
Based on the physics reviewed above, the scaling of the discharge is relatively straightforward. The desired discharge voltage xcfx86d is treated as a design parameter, because it directly determines the ion velocity (and hence specific impulse of the thruster), often dictated, for example, by satellite mission objectives.
The assumption that the electron temperature can be preserved with proper scaling is justified, if it is established that for a reduction of the total power by some factor xcex6, the rates of energy loss and thrust power are correspondingly reduced by the same factor. The reduction in discharge power without a reduction in the discharge voltage implies a reduction in the overall discharge current. However, for proper geometric scaling, the area is correspondingly reduced by the factor xcex62, such that the current densities must be increased by the factor 1/xcex6. The necessary scaling in the ion current density (and hence thrust power) is achieved if the plasma density is correspondingly increased, since the velocity is unchanged. The necessary scaling in the axial electron current density is achieved if the axial electron drift velocity, Ved, is arguably scale-invariant. As described previously (see W. A. Hargus, Jr., et al., cited above) both the anomalous Bohm transport and wall collisions will give rise to drift velocities that are scale-invariant. The axial drift velocity associated with Bohm transport is determined by the ratio of the electric field strength E, to the magnetic field strength B:                               V                      ed            Bohm                          =                                            e                              16                ⁢                B                                      ⁢            E                    ∼                      E            B                                              (        6        )            
which is preserved through a geometric scaling. If the cross-field transport is largely controlled by wall collisions, then, for highly magnetized electrons (xcfx89ce=eB/me greater than  greater than Vwall=Ce/W, the wall scattering frequency) (here, Ce is the mean thermal electron speed, which is preserved if the temperature is preserved, and e and me are the charge and mass of the electron, respectively), the axial electron drift velocity is approximately:                               V                      ed            Wall                          =                                            eEv              wall                                                      m                e                            ⁢                              ω                ce                2                                              ∼          EW                                    (        7        )            
which is also preserved with the proper geometric scaling, because the magnetic field scales as Bxcx9c1/w, as described above. The increased electron number density (by the factor 1/xcex6) is achieved because the corresponding decrease in the mass flow rate results in an increase in na, since the area is decreased by the factor xcex62. This relies on the assumption that the ionization fraction is preserved, which is reasonable if the ratio of time scales presented in Eqn. (5) is also preserved.
To preserve the electron temperature, the electron energy loss rates also scale in proportion to the decrease in power. The necessary scaling is obtained, if the dominant energy loss mechanism is through wall collisions. It is noteworthy that volumetric ionization also satisfies the scaling condition, because the energy loss rate through ionization is:
Ei=nenaxcex1iVcxcex5ixcx9cxcex6xe2x80x83xe2x80x83(8)
Here, Vc is the channel volume and xcex5i, the ionization energy of xenon. One undesirable consequence of the geometric scaling for operation at reduced power levels is an increase in heat flux to the channel walls (see V. Khayms and M. Martinez-Sanchez, xe2x80x9cDesign of a Miniaturized Hall Thruster for Microsatellites,xe2x80x9d AIAA-96-3291, 32nd Joint Propulsion Conference, Jul. 1-3, 1996, Lake Buena Vista, Fla.). Because the power is reduced by the scaling factor xcex6 and the wall area reduced by xcex62, the heat flux to the walls increases by a factor of 1/xcex6. This scaling consequence is potentially problematic for very low power (and consequently reduced size) Hall plasma thrusters.
It is noteworthy that the decreased residence time of the neutral xenon in the channel (see Eqn. (4)) should result in a shift to high frequencies in the characteristic breathing instability often seen in the 7-10 kHz frequency range in higher power devices (see J. M. Fife, M. Martinez-Sanchez, and J. J. Szabo, xe2x80x9cNumerical Study of Low Frequency Discharge Oscillations in Hall Thrusters,xe2x80x9d AIAA-97-3052, 33rd Joint Propulsion Conference Jul. 6-9, 1997 Seattle, Wash.). Current oscillation frequencies in the discharge are consistent with the nearly 1/10th scaling described in the above analysis.
In summary, it is desirable to provide a method to scale the power of a Hall thruster by some arbitrary factor xcex6, such that the characteristic scale lengths of the thruster and mass flow rates are scaled by the same factor, xcex6. The appropriate adjustment to the magnetic field (preserving its shape) is to increase it by the factor 1/xcex6. With these scaling laws, according to the analysis described above, the electron temperature should be preserved, as well as the ratio of electron current to ion current.
Accordingly, it is desired to design Hall thrusters that are smaller, more compact, and more efficient at low power than present coaxial Hall thrusters. It is further desired to design such Hall thrusters with larger specific thrust area ratios and simpler magnetic circuit configurations than those of present coaxial Hall thrusters. It is moreover desired to design such Hall thrusters, which can be combined in a modular array to extend the operating envelope of a propulsion system. Finally, it is desired that such Hall thrusters perform more ruggedly and reliably than present coaxial Hall thrusters.
Accordingly, it is a primary object of the present invention to provide a method to design Hall thrusters that are smaller, more compact, and more efficient at low power than present coaxial Hall thrusters. It is a further object to design such Hall thrusters with larger specific thrust area ratios and simpler magnetic circuit configurations than those of present coaxial Hall thrusters. It is moreover an object to design such Hall thrusters, which can be combined in a modular array to extend the operating envelope of a propulsion system. Finally, it is an object for such Hall thrusters to perform more ruggedly and reliably than present coaxial Hall thrusters.
These objects and advantages are attained by a Hall plasma thruster design having an electric field oriented parallel to a first axis and a magnetic field oriented substantially orthogonal to the electric field. The Hall thruster design has a substantially linear channel having a length mutually orthogonal to the electric and magnetic fields, an open exit face extending substantially the entire length of the channel, and channel walls extending perpendicular to the open exit face. The channel has a base substantially parallel to the exit face, which is separated from the open exit face by a channel depth. The Hall thruster additionally has a source of electrons external and adjacent to the channel exit face, providing electrons that undergo open electron drift within the channel in a direction substantially parallel to the channel length, under combined influence of the orthogonal electric and magnetic fields. A source of neutral particles, typically xenon atoms, is positioned adjacent the base of the discharge channel. The neutral particles enter the channel and undergo collisions with the electrons, resulting in the ionization of a portion of the neutral particles.
The walls of the channel are constructed of electrically insulating material, preferably a ceramic such as alumina or boron nitride. The electric and magnetic field values, as well as aspect ratios between channel length and channel depth are selected in accordance with a scaling methodology.
In operation, a plasma thruster in accordance with an embodiment of the present invention is placed in a vacuum environment having a background pressure preferably not greater than approximately 10xe2x88x924 Torr. The ionized particles are accelerated by the electric field and are ejected from the discharge channel through the open exit face. A portion of the ejected ions combine with electrons to form neutral particles, which serve as a neutral propellant.
Linear Hall thrusters simplify magnetic circuit configurations, permitting the use of permanent magnets. Linear thrusters further enable efficient stacking of thrusters to provide modular arrays. This modular approach can be used to maintain operation at maximum efficiencies by selectively turning individual linear thrusters on and off to change the thrust level, rather than changing the operating point of a single thruster.